Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T14:13:42.877Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental study on the kinetics of granular gases under microgravity

Published online by Cambridge University Press:  10 December 2009

SOICHI TATSUMI ,
YOSHIHIRO MURAYAMA ,
HISAO HAYAKAWA  and
MASAKI SANO
SOICHI TATSUMI*
Affiliation:
Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
YOSHIHIRO MURAYAMA
Affiliation:
Department of Applied Physics, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei-shi, Tokyo 184-8588, Japan
HISAO HAYAKAWA
Affiliation:
Yukawa Institute for Theoretical Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
MASAKI SANO
Affiliation:
Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The kinetics of granular gases, including both freely cooling and steadily driven systems, is studied experimentally in quasi-two-dimensional cells. Under microgravity conditions achieved inside an aircraft flying parabolic trajectories, the frictional force is reduced. In both the freely cooling and steadily driven systems, we confirm that the velocity distribution function has the form exp(−α|v|β). The value of exponent β is close to 1.5 for the driven system in a highly excited case, which is consistent with theory derived under the assumption of the existence of the white-noise thermostat (van Noije & Ernst, Gran. Mat., vol. 1, 1998, p. 5764). In the freely cooling system, the value of β evolves from 1.5 to 1 as the cooling proceeds, and the system's energy decays algebraically (Tg = T0(1 + t/τ)−2), agreeing with Haff's law (Haff, J. Fluid Mech., vol. 134, 1983, p. 401430).

JFM classification

Rarefied Gas Flow: Kinetic theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 521 - 539
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ahmad, S. R. & Puri, S. 2006 Velocity distributions in a freely evolving granular gas. Euro. Phys. Lett. 75 (1), 56–62.CrossRefGoogle Scholar
Ahmad, S. R. & Puri, S. 2007 Velocity distributions and aging in a cooling granular gas. Phys. Rev. E 75, 031302.CrossRefGoogle Scholar
Aranson, I. S. & Olafsen, J. S. 2002 Velocity fluctuations in electrostatically driven granular media. Phys. Rev. E 66, 061302.CrossRefGoogle ScholarPubMed
Aspelmeier, T., Huthmann, M. & Zippelius, A. 2001 Free Cooling of Particles with Rotational Degrees of Freedom, Chapter 1, pp. 31–58. Lecture Notes in Physics, vol. 564. Springer.CrossRefGoogle Scholar
Baxter, G. W. & Olafsen, J. S. 2003 Kinetics: gaussian statistics in granular gases. Nature 425, 680.CrossRefGoogle ScholarPubMed
Baxter, G. W. & Olafsen, J. S. 2007 Experimental evidence for molecular chaos in granular gases. Phys. Rev. Lett. 99, 028001.CrossRefGoogle ScholarPubMed
Blair, D. L. & Kudrolli, A. 2001 Velocity correlations in dense granular gases. Phys. Rev. E 64, 050301(R).CrossRefGoogle ScholarPubMed
Brilliantov, N. V., Poöschel, T., Kranz, W. T. & Zippelius, A. 2007 Translations and rotations are correlated in granular gases. Phys. Rev. Lett. 98, 128001.CrossRefGoogle ScholarPubMed
Brilliantov, N. V. & Pöschel, T. 2000 Velocity distribution in granular gases of viscoelastic particles. Phys. Rev. E 61 (5), 5573–5587.CrossRefGoogle ScholarPubMed
Brilliantov, N. V. & Pöschel, T. 2004 Kinetic Theory of Granular Gases. Oxford University Press.CrossRefGoogle Scholar
Das, S. K. & Puri, S. 2003 Kinetics of inhomogeneous cooling in granular fluids. Phys. Rev. E 68, 011302.CrossRefGoogle ScholarPubMed
Duran, J. 2000 Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials Series. Springer.CrossRefGoogle Scholar
Ernst, M. H., Trizac, E. & Barrat, A. 2006 The Boltzmann equation for driven systems of inelastic soft spheres. J. Stat. Phys 124 (2–4), 549–586.CrossRefGoogle Scholar
Esipov, S. E. & Pöschel, T. 1997 The granular phase diagram. J. Stat. Phys. 86 (5/6), 1385–1395.CrossRefGoogle Scholar
Falcon, E., Aumaître, S., Évesque, P., Palencia, F., Lecoutre-Chabot, C., Fauve, S., Beysens, D. & Garrabos, Y. 2006 Collision statistics in a dilute granular gas fluidized by vibrations in low gravity. Europhys. Lett. 74 (5), 830–836.CrossRefGoogle Scholar
Fiscina, J. E. & Cáceres, M. O. 2007 Evaporation transition in vibro-fluidized granular matter. Europhys. Lett. 80, 14007.CrossRefGoogle Scholar
Géminard, J.-C. & Laroche, C. 2004 Pressure measurement in two-dimensional horizontal granular gases. Phys. Rev. E 70, 021301.CrossRefGoogle ScholarPubMed
Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267–293.CrossRefGoogle Scholar
Goldhirsch, I., Noskowicz, S. H. & Bar-Lev, O. 2005 Nearly smooth granular gases. Phys. Rev. Lett. 95 (6), 068002.CrossRefGoogle ScholarPubMed
Goldhirsch, I. & Zanneti, G. 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70 (11), 1619–1622.CrossRefGoogle ScholarPubMed
Goldshtein, A. & Shapiro, M. 1995 Mechanics of collisional motion of granular materials. Part 1. General hydrodynamics equations. J. Fluid Mech. 282, 75–114.CrossRefGoogle Scholar
Haff, P. K. 1983 Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401–430.CrossRefGoogle Scholar
Hayakawa, H. & Kawarada, A. 2005 Granular gas in an experimental accessible setup. In Powders and Grains, vol. 2, pp. 1103–1106. A. A. Bakema Publ., Leiden.Google Scholar
Herbst, O., Cafiero, R., Zippelius, A., Hermann, H. J. & Luding, S. 2005 A driven two-dimensional granular gas with coulomb friction. Phys. Fluids 17, 107102.CrossRefGoogle Scholar
Huthmann, M. & Zippelius, A. 1997 Dynamics of inelastically colliding rough spheres: relaxation of translational and rotational energy. Phys. Rev. E 56 (6), R6275.CrossRefGoogle Scholar
Jaeger, H. M., Nagel, S. R. & Behringer, R. P. 1996 Granular solids, liquids, and gases. Rev. Mod. Phys. 68 (4), 1259–1273.CrossRefGoogle Scholar
Jenkins, J. T. & Richman, M. W. 1985 Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28 (12), 3485.CrossRefGoogle Scholar
Jenkins, J. T. & Zhang, C. 2002 Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14 (3), 1228.CrossRefGoogle Scholar
Kawahara, R. & Nakanishi, H. 2004 Effects of velocity correlation on early stage of free cooling process of inelastic hard sphere system. J. Phys. Soc. Japan 73 (1), 68–75.CrossRefGoogle Scholar
Kawarada, A. & Hayakawa, H. 2004 Non-Gaussian velocity distribution function in a vibrating granular bed. J. Phys. Soc. Japan 73 (8), 2037–2040.CrossRefGoogle Scholar
Król, P. & Król, B. 2006 Determination of free surface energy values for ceramic materials and polyurethane surface-modifying aqueous emulsions. J. Eur. Ceram. Soc. 26 (12), 2241–2248.CrossRefGoogle Scholar
Kudrolli, A., Wolpert, M. & Gollub, J. P. 1997 Cluster formation due to collisions in granular material. Phys. Rev. Lett. 78 (7), 1383–1386.CrossRefGoogle Scholar
Labous, L., Rosato, A. D. & Dave, R. N. 1997 Measurements of collisional properties of spheres using high-speed video analysis. Phys. Rev. E 56 (5), 5717–5725.CrossRefGoogle Scholar
Losert, W., Cooper, D. G. W., Delour, J., Kudrolli, A. & Gollub, J. P. 1999 Velocity statistics in excited granular media. Chaos 9 (3), 682–690.CrossRefGoogle ScholarPubMed
Luding, S., Huthmann, M., McNamara, S. & Zippelius, A. 1998 Homogeneous cooling of rough, dissipative particles: theory and simulations. Phys. Rev. E 58 (3), 3416–3425.CrossRefGoogle Scholar
Maass, C. C., Isert, N., Maret, G. & Aegerter, C. M. 2008 Experimental investigation of the freely cooling granular gas. Phys. Rev. Lett. 100, 248001.CrossRefGoogle ScholarPubMed
McNamara, S. & Young, W. R. 1994 Inelastic collapse in two dimensions. Phys. Rev. E 50 (1), R28–R31.CrossRefGoogle ScholarPubMed
McNamara, S. & Young, W. R. 1996 Dynamics of a freely evolving, two-dimensional granular medium. Phys. Rev. E 53 (5), 5089–5100.CrossRefGoogle ScholarPubMed
Miller, S. & Luding, S. 2004 Cluster growth in two- and three-dimensional granular gases. Phys. Rev. E 69, 031305.CrossRefGoogle ScholarPubMed
Mischeler, S. & Mouhot, C. 2006 Cooling process for inelastic Boltzmann equations for hard spheres. Part I. Self-similar solutions and tail behaviour. J. Stat. Phys 124 (2–4), 703–746.CrossRefGoogle Scholar
Mischeler, S., Mouhot, C. & Richard, M. R. 2006 Cooling process for inelastic Boltzmann equations for hard spheres. Part I. The Cauchy problem. J. Stat. Phys 124 (2–4), 655–702.CrossRefGoogle Scholar
Moon, S. J., Swift, J. B. & Swinney, H. L. 2004 Steady-state velocity distributions of an oscillated granular gas. Phys. Rev. E 69, 011301.CrossRefGoogle ScholarPubMed
Murayama, Y. & Sano, M. 1998 Transition from Gaussian to non-Gaussian velocity distribution functions in a vibrated granular bed. J. Phys. Soc. Japan 67 (6), 1826–1829.CrossRefGoogle Scholar
Nie, X., Ben-Naim, E. & Chen, S. 2002 Dynamics of freely cooling granular gases. Phys. Rev. Lett. 89 (20), 204301.CrossRefGoogle ScholarPubMed
Olafsen, J. S. & Urbach, J. S. 1998 Clustering, order, and collapse in a driven granular monolayer. Phys. Rev. Lett. 81 (20), 4369–4372.CrossRefGoogle Scholar
Olafsen, J. S. & Urbach, J. S. 1999 Velocity distributions and density fluctuations in a granular gas. Phys. Rev. E 60 (3), R2468–R2471.CrossRefGoogle Scholar
Painter, B., Dutt, M. & Behringer, R. P. 2003 Energy dissipation and clustering for a cooling granular material on a substrate. Physica D 175 (1), 43–68.CrossRefGoogle Scholar
Pöschel, T., Brilliantov, N. V. & Formella, A. 2006 Impact of high-energy tails on granular gas properties. Phys. Rev. E 74, 041302.CrossRefGoogle ScholarPubMed
Reis, P. M., Ingale, R. A. & Shattuck, M. D. 2007 Forcing independent velocity distributions in an experimental granular fluid. Phys. Rev. E 75, 051311.CrossRefGoogle Scholar
Rouyer, F. & Menon, N. 2000 Velocity fluctuations in a homogeneous two-dimensional granular gas in steady state. Phys. Rev. Lett. 85 (17), 3676–3679.CrossRefGoogle Scholar
Saitoh, K. & Hayakawa, H. 2007 Rheology of a granular gas under a plane shear. Phys. Rev. E 75 (2), 021302.CrossRefGoogle Scholar
Santos, A. 2003 Transport coefficients of d-dimensional inelastic Maxwell models. Physica A 321 (3), 442.CrossRefGoogle Scholar
Santos, A., Brey, J. J., Kim, C. S. & Dufty, J. W. 1989 Velocity distribution for a gas with steady heat flow. Phys. Rev. A 39 (1), 320–327.CrossRefGoogle ScholarPubMed
Thornton, C. & Ning, Z. 1998 A theoretical model for the stick/bounce behaviour of adhesive, elastic–plastic spheres. Powder Technol. 99 (2), 154–162.CrossRefGoogle Scholar
van Noije, T. P. C. & Ernst, M. H. 1998 Velocity distributions in homogeneous granular fluids: the free and the heated case. Gran. Mat. 1, 57–64.CrossRefGoogle Scholar
van Noije, T. P. C., Ernst, M. H. & Brito, R 1998 Ring kinetic theory for an idealized granular gas. Physica A 251 (1), 266–283.CrossRefGoogle Scholar
van Zon, J. S., Kreft, J., Goldman, Daniel I., Miracle, D., Swift, J. B. & Swinney, Harry L. 2004 Crucial role of sidewalls in velocity distributions in quasi-two-dimensional granular gases. Phys. Rev. E 70, 040301(R).CrossRefGoogle ScholarPubMed
van Zon, J. S. & MacKintosh, F. C. 2005 Velocity distributions in dilute granular systems. Phys. Rev. E 72, 051301.CrossRefGoogle ScholarPubMed
Villani, C. 2006 Mathematics of granular materials. J. Stat. Phys. 124 (2–4), 781–822.CrossRefGoogle Scholar
Wang, H.-Q. & Menon, N. 2008 Heating mechanism affects equipartition in a binary granular system. Phys. Rev. Lett. 100, 158001.CrossRefGoogle Scholar
Weir, G. & Tallon, S. 2005 The coefficient of restitution for normal incident, low velocity particle impacts. Chem. Engng Sci. 60 (13), 3637–3647.CrossRefGoogle Scholar
Xu, H., Reeves, A. P. & Louge, M. Y. 2004 Measurement errors in the mean and fluctuation velocities of spherical grains from a computer analysis of digital images. Rev. Sci. Instrum. 75 (4), 811.CrossRefGoogle Scholar